If S is the sum of first 732 prime numbers , then it is always divisible by ?

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of them

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is C None of them
Total prime numbers $= 732$
Except $2$ all other prime numbers are odd numbers.
We have $731$ odd prime numbers.
On adding these $731$ numbers , we get an odd number .
And, odd number + even number = An odd number.
S = An odd number.
Hence, an odd number cannot be divisible by an even number .
Therefore, for none of $2, 4$ and $6$ can divide $S$ .

Suggest Corrections

Similar questions

If N is the sum of first 13986 prime numbers, then N is always divisible by:

Q. If

N

is the sum of first

13, 986

prime numbers, then N is always divisible by -

Q. If N is the sum of first 13986 prime numbers, then N is always divisible by:

Q. Which of the following statements are true?

(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is divisible by both 9 and 10, it must be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divide their sum exactly.
(ix) If two numbers are co-prime, at least one of them must be a prime number
(x) The sum of two consecutive odd numbers is always divisible by 4.

Which of the following statements are true ?
(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is bivisible by both 9 and 10, ut nyst be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divede their sum exactly.
(ix) If two numbers are co-prime , at least one of them must be a prime number.
(x) The sum of two consecutive odd numbers is always divisible by 4.

Join BYJU'S Learning Program